IEEE Geoscience and Remote Sensing Magazine - June 2019 - 16

variability as well, with an increasing secondary illumination impact for higher obstruction levels.
Although BRDF effects are intrinsic to the target material (and have been described in the "Intrinsic Target Variability" section), spectral variability due to BRDF also has
an environmental flavor. Indeed, variability due to variations in illumination and acquisition geometry is deeply
intertwined with variability due to the non-Lambertian
nature of target materials. Thus, to provide some insight
into environmentally induced spectral variability for nonLambertian targets, a further illustrative example, using the
same parameters as used previously, is shown in Figure 5.
Two glossy targets taken from the Cornell BRDF database
[56] are considered here: specifically, a target painted with a
"garnet red" lacquer [Figure 5(a) and (b), top panels] and a
glossier target painted with a "mystique" lacquer [Figure 5(c)
and (d), bottom panels]. Here, the left panels in Figure 5(a)
and (c) plot the target BRDFs for a fixed illumination direction (as before, i i = i i . 31c) for varying orientation angle
i O. The values of i O were chosen to correspond to the same
sensor-viewing angles, i v = 180c - i O, used in the previous example. The oblique specular geometry (i v = 149c)
is not included in the analysis, because the Cornell BRDF
data do not include measurements of specular reflectance; if
needed, however, they could be introduced by adding a term
ruled by the Fresnel reflectance [57].
As is evident from the target BRDFs, the non-Lambertian
effects are different for the different targets. In Figure 5(a),
the effect is mostly just a scaling of the reflectance function
for the "garnet red" target, with higher reflectance for nadir
viewing. In Figure 5(c), however, the effect produces actual
changes of color for the "mystique" target, which exhibits a
strong reflectance contribution of approximately 500 nm
for nadir and 20° off-nadir views and strong contributions
at shorter and higher wavelengths for the 40° and 60° offnadir views. Figure 5(b) and (d) plots the sensor-reaching
radiance for the sensor-viewing angles matching the orientation angles varied in Figure 5(a) and (c). The figures
clearly show that environmental effects blend with the

TABLE 3. PARAMETERS USED IN THE EXAMPLE IN FIGURE 4.
ATMOSPHERIC MODEL

16

Midlatitude
summer

VISIBILITY (km)

AEROSOL MODEL

Maritime

WV SCALING FACTOR (WVsf )

SENSOR ELEVATION (km)

1.250

ADJACENCY

TARGET ALTITUDE (km)

0

OBSTACLES AND
OBSTRUCTION

TARGET LATITUDE (°)

43.85 north

VIEWING ANGLE (i v) [°]

TARGET LONGITUDE (°)

10.25 east

SHADOWING (a sh)

DATE

9 May 2013

SLOPE ELEVATION (i sl) [°]

GMT TIME (h)

12.65

SLOPE/SUN RELATIVE AZIMUTH (z sl - z ) [°]

BRDF effects in the at-sensor spectral radiances. In fact,
whereas the mostly path-radiance-driven effects already
observed in Figure 4(d) (i.e., increased radiance, especially
at shorter wavelengths for longer paths due to oblique sensing) are clearly evident (and stronger with respect to the
previous examples due to the very low reflectance of the
targets), these are combined with the effects of the different spectral characteristics that the target materials intrinsically have for different viewing angles.
In Figure 5(b), the path-radiance-driven spectral radiance increase at shorter wavelengths, strongly evident for
the most oblique case (i v = 120c), is less evident for the
other off-nadir viewing angles because the higher overall ref lectance for a nadir view [evident in Figure
5(a)] determines a stronger radiance contribution, even
though the increase due to path radiance is lower than in
the off-nadir cases. Similar considerations can be made
in Figure  5(d), where the stronger reflectance contributions around 500 nm for the "mystique" target at nadir
and 20° off-nadir views lead to radiance contributions
around 500 nm that are stronger than or equal to the 40°
off-nadir case.
These simple examples demonstrate that the causes of
nonnegligible spectral variability are multifold, and the
corresponding effects on the target spectra manifest themselves in complicated ways that can go beyond straightforward scaling or offsets. The aggregation of multiple diverse
environmental effects-in addition to the spatial nonstationarity and temporal nonstationarity of the sources of
these effects-makes environmentally induced spectral
variability a true challenge for effective hyperspectral image exploitation.
So far, we have examined the major sources of environmentally induced variability occurring when spectral
radiance is measured in the VNIR-SWIR range. If data collection takes place with a sensor operating in the LWIR,
a different radiative transfer model should be considered
[58], [59], and a further source of variability comes into
play, namely, temperature (primarily of the surface, but also
of the atmosphere and the adjacent areas), which exhibits further temporal
and spatial nonstationarity.
We conclude this section, which
{5, 10, 23, 35}
focused on the main sources of variability for the sensor-reaching spec{0.5, 1, 2}
tral radiance Ls (m), with a reminder
ra = {0, r Ol, rRl, rAl}
that Ls (m) as expressed here is the
robst = {0, r Ol, rAl}
radiance entering the sensor, which
F = {0, 0.85, 0.70}
is not precisely equal to the spectral
{120, 140, 160, 180}
radiance actually measured by the
sensor. Although beyond the scope
{0, 0.5, 1}
of this survey, radiance collection
{0, ±15, ±30}
by the sensor acquisition system can
0
introduce further variability to the
measured signal (e.g., due to sensor
noise, smile and keystone effects,
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

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IEEE Geoscience and Remote Sensing Magazine - June 2019

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